I have written a piece stemming from an idea about a particular process that leads to the attainment of magical abilities. The working title was written for the small, 250 word, treatise that I used to get my thoughts on the subject codified before starting the narrative. Now with the finished piece in the 1600 word range the title doesn't work particularly well and in fact I'm not sure if the treatise itself has has a role in the overall piece or not. My question is what aspects of the story, if any, have the greatest bearing on changing the title to something that encompasses the finished tale as a whole?
Every good story title is a come hither word or phrase. Phrases are usually better because they can impact more of an idea than a single word. Yes it should encapsulate an important aspect of the story, but it should intrigue the potential reader to want to read the story.
Since your story, all 1600 words of it, are about someone who goes through a process of gaining magical abilities, then the title should hint, at the very least, at what that process is, or its outcome.
Sir Arthur Conan Doyle, best known as the author of the sherlock Holmes stories, apparently argued that a good title should be both specific and distinctive to the story it decorates.
For example, a title like "The Tangled Web" could be about almost anything. It could be a love gone wrong, the consequences of telling lies, a spy network, the collapse of the internet, disaster on a fishing trip, and so-on and so-on. Whereas, "The Speckled Band" and "The Red-Headed League" are the titles of two Sherlock Holmes stories and they each refer specifically to important elements in their stories. They are distinctive, intriguing, and highlight something important. They refer to a swamp adder and a fake organization respectively.
Find what is specific, distinctive, intriguing and important in your story and start devising titles. After all, why stop at one? You may need to create several titles before you find the one you most like. Few of us get it right the first time. Give it a go.